x3o3o     
               
x3o3x     x3o3x

       o o3x    o o3o  
                       
                       
                       
x o3x    x x3x    x x3o

This polyteron is obtained as tet-first segment of spix wrt. those tets, which are at the margin between 2 spids.

Incidence matrix according to Dynkin symbol

ox ox3oo3xx&#x   → height = sqrt(3/8) = 0.612372
(tet || cope)

o. o.3o.3o.    | 4  * | 3  6  0  0  0 | 3  3  6 12  0  0 0  0 0 | 1  3  6 2  6 6 0 0 0 0 | 1 3 3 2 0
.o .o3.o3.o    | * 24 | 0  1  1  2  2 | 0  1  2  2  2  2 1  2 1 | 0  2  2 1  2 1 1 2 1 1 | 1 2 1 1 1
---------------+------+---------------+-------------------------+------------------------+----------
.. .. .. x.    | 2  0 | 6  *  *  *  * | 2  0  0  4  0  0 0  0 0 | 1  0  2 0  2 4 0 0 0 0 | 0 1 2 2 0
oo oo3oo3oo&#x | 1  1 | * 24  *  *  * | 0  1  2  2  0  0 0  0 0 | 0  2  2 1  2 1 0 0 0 0 | 1 2 1 1 0
.x .. .. ..    | 0  2 | *  * 12  *  * | 0  1  0  0  2  2 0  0 0 | 0  2  2 0  0 0 1 2 1 0 | 1 2 1 0 1
.. .x .. ..    | 0  2 | *  *  * 24  * | 0  0  1  0  1  0 1  1 0 | 0  1  0 1  1 0 1 1 0 1 | 1 1 0 1 1
.. .. .. .x    | 0  2 | *  *  *  * 24 | 0  0  0  1  0  1 0  1 1 | 0  0  1 0  1 1 0 1 1 1 | 0 1 1 1 1
---------------+------+---------------+-------------------------+------------------------+----------
.. .. o.3x.    | 3  0 | 3  0  0  0  0 | 4  *  *  *  *  * *  * * | 1  0  0 0  0 2 0 0 0 0 | 0 0 1 2 0
ox .. .. ..&#x | 1  2 | 0  2  1  0  0 | * 12  *  *  *  * *  * * | 0  2  2 0  0 0 0 0 0 0 | 1 2 1 0 0
.. ox .. ..&#x | 1  2 | 0  2  0  1  0 | *  * 24  *  *  * *  * * | 0  1  0 1  1 0 0 0 0 0 | 1 1 0 1 0
.. .. .. xx&#x | 2  2 | 1  2  0  0  1 | *  *  * 24  *  * *  * * | 0  0  1 0  1 1 0 0 0 0 | 0 1 1 1 0
.x .x .. ..    | 0  4 | 0  0  2  2  0 | *  *  *  * 12  * *  * * | 0  1  0 0  0 0 1 1 0 0 | 1 1 0 0 1
.x .. .. .x    | 0  4 | 0  0  2  0  2 | *  *  *  *  * 12 *  * * | 0  0  1 0  0 0 0 1 1 0 | 0 1 1 0 1
.. .x3.o ..    | 0  3 | 0  0  0  3  0 | *  *  *  *  *  * 8  * * | 0  0  0 1  0 0 1 0 0 1 | 1 0 0 1 1
.. .x .. .x    | 0  4 | 0  0  0  2  2 | *  *  *  *  *  * * 12 * | 0  0  0 0  1 0 0 1 0 1 | 0 1 0 1 1
.. .. .o3.x    | 0  3 | 0  0  0  0  3 | *  *  *  *  *  * *  * 8 | 0  0  0 0  0 1 0 0 1 1 | 0 0 1 1 1
---------------+------+---------------+-------------------------+------------------------+----------
.. o.3o.3x.    ♦ 4  0 | 6  0  0  0  0 | 4  0  0  0  0  0 0  0 0 | 1  *  * *  * * * * * * | 0 0 0 2 0
ox ox .. ..&#x ♦ 1  4 | 0  4  2  2  0 | 0  2  2  0  1  0 0  0 0 | * 12  * *  * * * * * * | 1 1 0 0 0
ox .. .. xx&#x ♦ 2  4 | 1  4  2  0  2 | 0  2  0  2  0  1 0  0 0 | *  * 12 *  * * * * * * | 0 1 1 0 0
.. ox3oo ..&#x ♦ 1  3 | 0  3  0  3  0 | 0  0  3  0  0  0 1  0 0 | *  *  * 8  * * * * * * | 1 0 0 1 0
.. ox .. xx&#x ♦ 2  4 | 1  4  0  2  2 | 0  0  2  2  0  0 0  1 0 | *  *  * * 12 * * * * * | 0 1 0 1 0
.. .. oo3xx&#x ♦ 3  3 | 3  3  0  0  3 | 1  0  0  3  0  0 0  0 1 | *  *  * *  * 8 * * * * | 0 0 1 1 0
.x .x3.o ..    ♦ 0  6 | 0  0  3  6  0 | 0  0  0  0  3  0 2  0 0 | *  *  * *  * * 4 * * * | 1 0 0 0 1
.x .x .. .x    ♦ 0  8 | 0  0  4  4  4 | 0  0  0  0  2  2 0  2 0 | *  *  * *  * * * 6 * * | 0 1 0 0 1
.x .. .o3.x    ♦ 0  6 | 0  0  3  0  6 | 0  0  0  0  0  3 0  0 2 | *  *  * *  * * * * 4 * | 0 0 1 0 1
.. .x3.o3.x    ♦ 0 12 | 0  0  0 12 12 | 0  0  0  0  0  0 4  6 4 | *  *  * *  * * * * * 2 | 0 0 0 1 1
---------------+------+---------------+-------------------------+------------------------+----------
ox ox3oo ..&#x ♦ 1  6 | 0  6  3  6  0 | 0  3  6  0  3  0 2  0 0 | 0  3  0 2  0 0 1 0 0 0 | 4 * * * *
ox ox .. xx&#x ♦ 2  8 | 1  8  4  4  4 | 0  4  4  4  2  2 0  2 0 | 0  2  2 0  2 0 0 1 0 0 | * 6 * * *
ox .. oo3xx&#x ♦ 3  6 | 3  6  3  0  6 | 1  3  0  6  0  3 0  0 2 | 0  0  3 0  0 2 0 0 1 0 | * * 4 * *
.. ox3oo3xx&#x ♦ 4 12 | 6 12  0 12 12 | 4  0 12 12  0  0 4  6 4 | 1  0  0 4  6 4 0 0 0 1 | * * * 2 *
.x .x3.o3.x    ♦ 0 24 | 0  0 12 24 24 | 0  0  0  0 12 12 8 12 8 | 0  0  0 0  0 0 4 6 4 2 | * * * * 1

oxx3ooo3xxx&#x   → height(1,2) = height(1,3) = sqrt(5/8) = 0.790569
                   height(2,3) = 1

o..3o..3o..    | 4  *  * | 3  3  3  0  0  0  0  0 | 3  3  6  3  3  6 0 0 0  0  0 0 0 0 | 1 1 3 3  3  6 1 3 3 0 0 0 0 0 | 1 1 3 3 1 0
.o.3.o.3.o.    | * 12  * | 0  1  0  2  2  1  0  0 | 0  2  2  1  0  0 1 2 1  2  2 0 0 0 | 0 1 2 1  2  2 0 0 0 1 1 2 1 0 | 1 1 2 1 0 1
..o3..o3..o    | *  * 12 | 0  0  1  0  0  1  2  2 | 0  0  0  1  2  2 0 0 0  2  2 1 2 1 | 0 0 0 0  2  2 1 2 1 0 1 2 1 1 | 0 1 2 1 1 1
---------------+---------+------------------------+------------------------------------+-------------------------------+------------
... ... x..    | 2  0  0 | 6  *  *  *  *  *  *  * | 2  0  2  0  0  2 0 0 0  0  0 0 0 0 | 1 0 1 2  0  2 0 1 2 0 0 0 0 0 | 1 0 1 2 1 0
oo.3oo.3oo.&#x | 1  1  0 | * 12  *  *  *  *  *  * | 0  2  2  1  0  0 0 0 0  0  0 0 0 0 | 0 1 2 1  2  2 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0
o.o3o.o3o.o&#x | 1  0  1 | *  * 12  *  *  *  *  * | 0  0  0  1  2  2 0 0 0  0  0 0 0 0 | 0 0 0 0  2  2 1 2 1 0 0 0 0 0 | 0 1 2 1 1 0
.x. ... ...    | 0  2  0 | *  *  * 12  *  *  *  * | 0  1  0  0  0  0 1 1 0  1  0 0 0 0 | 0 1 1 0  1  0 0 0 0 1 1 1 0 0 | 1 1 1 0 0 1
... ... .x.    | 0  2  0 | *  *  *  * 12  *  *  * | 0  0  1  0  0  0 0 1 1  0  1 0 0 0 | 0 0 1 1  0  1 0 0 0 1 0 1 1 0 | 1 0 1 1 0 1
.oo3.oo3.oo&#x | 0  1  1 | *  *  *  *  * 12  *  * | 0  0  0  1  0  0 0 0 0  2  2 0 0 0 | 0 0 0 0  2  2 0 0 0 0 1 2 1 0 | 0 1 2 1 0 1
..x ... ...    | 0  0  2 | *  *  *  *  *  * 12  * | 0  0  0  0  1  0 0 0 0  1  0 1 1 0 | 0 0 0 0  1  0 1 1 0 0 1 1 0 1 | 0 1 1 0 1 1
... ... ..x    | 0  0  2 | *  *  *  *  *  *  * 12 | 0  0  0  0  0  1 0 0 0  0  1 0 1 1 | 0 0 0 0  0  1 0 1 1 0 0 1 1 1 | 0 0 1 1 1 1
---------------+---------+------------------------+------------------------------------+-------------------------------+------------
... o..3x..    | 3  0  0 | 3  0  0  0  0  0  0  0 | 4  *  *  *  *  * * * *  *  * * * * | 1 0 0 1  0  0 0 0 1 0 0 0 0 0 | 1 0 0 1 1 0
ox. ... ...&#x | 1  2  0 | 0  2  0  1  0  0  0  0 | * 12  *  *  *  * * * *  *  * * * * | 0 1 1 0  1  0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
... ... xx.&#x | 2  2  0 | 1  2  0  0  1  0  0  0 | *  * 12  *  *  * * * *  *  * * * * | 0 0 1 1  0  1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
ooo3ooo3ooo&#x | 1  1  1 | 0  1  1  0  0  1  0  0 | *  *  * 12  *  * * * *  *  * * * * | 0 0 0 0  2  2 0 0 0 0 0 0 0 0 | 0 1 2 1 0 0
o.x ... ...&#x | 1  0  2 | 0  0  2  0  0  0  1  0 | *  *  *  * 12  * * * *  *  * * * * | 0 0 0 0  1  0 1 1 0 0 0 0 0 0 | 0 1 1 0 1 0
... ... x.x&#x | 2  0  2 | 1  0  2  0  0  0  0  1 | *  *  *  *  * 12 * * *  *  * * * * | 0 0 0 0  0  1 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
.x.3.o. ...    | 0  3  0 | 0  0  0  3  0  0  0  0 | *  *  *  *  *  * 4 * *  *  * * * * | 0 1 0 0  0  0 0 0 0 1 1 0 0 0 | 1 1 0 0 0 1
.x. ... .x.    | 0  4  0 | 0  0  0  2  2  0  0  0 | *  *  *  *  *  * * 6 *  *  * * * * | 0 0 1 0  0  0 0 0 0 1 0 1 0 0 | 1 0 1 0 0 1
... .o.3.x.    | 0  3  0 | 0  0  0  0  3  0  0  0 | *  *  *  *  *  * * * 4  *  * * * * | 0 0 0 1  0  0 0 0 0 1 0 0 1 0 | 1 0 0 1 0 1
.xx ... ...&#x | 0  2  2 | 0  0  0  1  0  2  1  0 | *  *  *  *  *  * * * * 12  * * * * | 0 0 0 0  1  0 0 0 0 0 1 1 0 0 | 0 1 1 0 0 1
... ... .xx&#x | 0  2  2 | 0  0  0  0  1  2  0  1 | *  *  *  *  *  * * * *  * 12 * * * | 0 0 0 0  0  1 0 0 0 0 0 1 1 0 | 0 0 1 1 0 1
..x3..o ...    | 0  0  3 | 0  0  0  0  0  0  3  0 | *  *  *  *  *  * * * *  *  * 4 * * | 0 0 0 0  0  0 1 0 0 0 1 0 0 1 | 0 1 0 0 1 1
..x ... ..x    | 0  0  4 | 0  0  0  0  0  0  2  2 | *  *  *  *  *  * * * *  *  * * 6 * | 0 0 0 0  0  0 0 1 0 0 0 1 0 1 | 0 0 1 0 1 1
... ..o3..x    | 0  0  3 | 0  0  0  0  0  0  0  3 | *  *  *  *  *  * * * *  *  * * * 4 | 0 0 0 0  0  0 0 0 1 0 0 0 1 1 | 0 0 0 1 1 1
---------------+---------+------------------------+------------------------------------+-------------------------------+------------
o..3o..3x..    ♦ 4  0  0 | 6  0  0  0  0  0  0  0 | 4  0  0  0  0  0 0 0 0  0  0 0 0 0 | 1 * * *  *  * * * * * * * * * | 1 0 0 0 1 0
ox.3oo. ...&#x ♦ 1  3  0 | 0  3  0  3  0  0  0  0 | 0  3  0  0  0  0 1 0 0  0  0 0 0 0 | * 4 * *  *  * * * * * * * * * | 1 1 0 0 0 0
ox. ... xx.&#x ♦ 2  4  0 | 1  4  0  2  2  0  0  0 | 0  2  2  0  0  0 0 1 0  0  0 0 0 0 | * * 6 *  *  * * * * * * * * * | 1 0 1 0 0 0
... oo.3xx.&#x ♦ 3  3  0 | 3  3  0  0  3  0  0  0 | 1  0  3  0  0  0 0 0 1  0  0 0 0 0 | * * * 4  *  * * * * * * * * * | 1 0 0 1 0 0
oxx ... ...&#x ♦ 1  2  2 | 0  2  2  1  0  2  1  0 | 0  1  0  2  1  0 0 0 0  1  0 0 0 0 | * * * * 12  * * * * * * * * * | 0 1 1 0 0 0
... ... xxx&#x ♦ 2  2  2 | 1  2  2  0  1  2  0  1 | 0  0  1  2  0  1 0 0 0  0  1 0 0 0 | * * * *  * 12 * * * * * * * * | 0 0 1 1 0 0
o.x3o.o ...&#x ♦ 1  0  3 | 0  0  3  0  0  0  3  0 | 0  0  0  0  3  0 0 0 0  0  0 1 0 0 | * * * *  *  * 4 * * * * * * * | 0 1 0 0 1 0
o.x ... x.x&#x ♦ 2  0  4 | 1  0  4  0  0  0  2  2 | 0  0  0  0  2  2 0 0 0  0  0 0 1 0 | * * * *  *  * * 6 * * * * * * | 0 0 1 0 1 0
... o.o3x.x&#x ♦ 3  0  3 | 3  0  3  0  0  0  0  3 | 1  0  0  0  0  3 0 0 0  0  0 0 0 1 | * * * *  *  * * * 4 * * * * * | 0 0 0 1 1 0
.x.3.o.3.x.    ♦ 0 12  0 | 0  0  0 12 12  0  0  0 | 0  0  0  0  0  0 4 6 4  0  0 0 0 0 | * * * *  *  * * * * 1 * * * * | 1 0 0 0 0 1
.xx3.oo ...&#x ♦ 0  3  3 | 0  0  0  3  0  3  3  0 | 0  0  0  0  0  0 1 0 0  3  0 1 0 0 | * * * *  *  * * * * * 4 * * * | 0 1 0 0 0 1
.xx ... .xx&#x ♦ 0  4  4 | 0  0  0  2  2  4  2  2 | 0  0  0  0  0  0 0 1 0  2  2 0 1 0 | * * * *  *  * * * * * * 6 * * | 0 0 1 0 0 1
... .oo3.xx&#x ♦ 0  3  3 | 0  0  0  0  3  3  0  3 | 0  0  0  0  0  0 0 0 1  0  3 0 0 1 | * * * *  *  * * * * * * * 4 * | 0 0 0 1 0 1
..x3..o3..x    ♦ 0  0 12 | 0  0  0  0  0  0 12 12 | 0  0  0  0  0  0 0 0 0  0  0 4 6 4 | * * * *  *  * * * * * * * * 1 | 0 0 0 0 1 1
---------------+---------+------------------------+------------------------------------+-------------------------------+------------
ox.3oo.3xx.&#x ♦ 4 12  0 | 6 12  0 12 12  0  0  0 | 4 12 12  0  0  0 4 6 4  0  0 0 0 0 | 1 4 6 4  0  0 0 0 0 1 0 0 0 0 | 1 * * * * *
oxx3ooo ...&#x ♦ 1  3  3 | 0  3  3  3  0  3  3  0 | 0  3  0  3  3  0 1 0 0  3  0 1 0 0 | 0 1 0 0  3  0 1 0 0 0 1 0 0 0 | * 4 * * * *
oxx ... xxx&#x ♦ 2  4  4 | 1  4  4  2  2  4  2  2 | 0  2  2  4  2  2 0 1 0  2  2 0 1 0 | 0 0 1 0  2  2 0 1 0 0 0 1 0 0 | * * 6 * * *
... ooo3xxx&#x ♦ 3  3  3 | 3  3  3  0  3  3  0  3 | 1  0  3  3  0  3 0 0 1  0  3 0 0 1 | 0 0 0 1  0  3 0 0 1 0 0 0 1 0 | * * * 4 * *
o.x3o.o3x.x&#x ♦ 4  0 12 | 6  0 12  0  0  0 12 12 | 4  0  0  0 12 12 0 0 0  0  0 4 6 4 | 1 0 0 0  0  0 4 6 4 0 0 0 0 1 | * * * * 1 *
.xx3.oo3.xx&#x ♦ 0 12 12 | 0  0  0 12 12 12 12 12 | 0  0  0  0  0  0 4 6 4 12 12 4 6 4 | 0 0 0 0  0  0 0 0 0 1 4 6 4 1 | * * * * * 1